have one eye on (someone or something)

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have one eye on (someone or something)

To watch someone or something intermittently or half-heartedly while something else is happening. Unfortunately, I don't remember what that list said because I had one eye on the TV while Mom was trying to show it to me.
See also: eye, have, on, one

have one eye/half an eye on something

look at or watch something while doing something else, especially in a secret way so that other people do not notice: During his talk, most of the delegates had one eye on the clock.
See also: eye, half, have, on, one, something